ライブラリ登録: Guest
Begell Digital Portal Begellデジタルライブラリー 電子書籍 ジャーナル 参考文献と会報 リサーチ集
International Journal for Uncertainty Quantification
インパクトファクター: 4.911 5年インパクトファクター: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN 印刷: 2152-5080
ISSN オンライン: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2018021021
pages 383-403

DATA ASSIMILATION FOR NAVIER-STOKES USING THE LEAST-SQUARES FINITE-ELEMENT METHOD

Alexander Schwarz
Institut für Mechanik, University of Duisburg-Essen, Universitätsstraße 15, 45141 Essen, Germany
Richard P. Dwight
Aerodynamics Group, Faculty of Aerospace, TU Delft, P.O. Box 5058, 2600GB Delft, The Netherlands

要約

We investigate theoretically and numerically the use of the least-squares finite-element method (LSFEM) to approach data-assimilation problems for the steady-state, incompressible Navier-Stokes equations. Our LSFEM discretization is based on a stress-velocity-pressure (S-V-P) first-order formulation, using discrete counterparts of the Sobolev spaces H(div)×H1×L2 for the variables respectively. In general, S-V-P formulations are promising when the stresses are of special interest, e.g., for non-Newtonian, multiphase or turbulent flows. Resolution of the system is via minimization of a least-squares functional representing the magnitude of the residual of the equations. A simple and immediate approach to extend this solver to data assimilation is to add a data-discrepancy term to the functional. Whereas most data assimilation techniques require a large number of evaluations of the forward simulation and are therefore very expensive, the approach proposed in this work uniquely has the same cost as a single forward run. However, the question arises: what is the statistical model implied by this choice? We answer this within the Bayesian framework, establishing the latent background covariance model and the likelihood. Further we demonstrate that−in the linear case−the method is equivalent to application of the Kalman filter, and derive the posterior covariance. We practically demonstrate the capabilities of our method on a backward-facing step case. Our LSFEM formulation (without data) is shown to have good approximation quality, even on relatively coarse meshes−in particular with respect to mass conservation and reattachment location. Adding limited velocity measurements from experiment, we show that the method is able to correct for discretization error on very coarse meshes, as well as correct for the influence of unknown and uncertain boundary conditions.


Articles with similar content:

OUTLINE OF RESEARCH FOR INTERFACIAL AREA TRANSPORT PHENOMENA IN TWO-PHASE FLOW
Multiphase Science and Technology, Vol.15, 2003, issue 1-4
Mamoru Ishii
Influence of the numerical schemes on the flow states of a simplified heavy vehicle
ICHMT DIGITAL LIBRARY ONLINE, Vol.0, 2018, issue
Guglielmo Minelli, Sinisa Krajnovic, J. Zhang, A. Rao, Branislav Basara
Fast Deflation Methods with Applications to Two-Phase Flows
International Journal for Multiscale Computational Engineering, Vol.6, 2008, issue 1
Cornelis Vuik, J. M. Tang
ROBUST UNCERTAINTY QUANTIFICATION USING PRECONDITIONED LEAST-SQUARES POLYNOMIAL APPROXIMATIONS WITH l1-REGULARIZATION
International Journal for Uncertainty Quantification, Vol.6, 2016, issue 1
D. Lucor, A. Belme, Jan Van Langenhove
A STOPPING CRITERION FOR ITERATIVE SOLUTION OF STOCHASTIC GALERKIN MATRIX EQUATIONS
International Journal for Uncertainty Quantification, Vol.6, 2016, issue 3
Christophe Audouze , Pär Håkansson, Prasanth B. Nair